The Pontryagin maximum principle for solving Fokker–Planck optimal control problems

Tim Breitenbach () and Alfio Borzì ()
Additional contact information
Tim Breitenbach: Universität Würzburg
Alfio Borzì: Universität Würzburg

Computational Optimization and Applications, 2020, vol. 76, issue 2, No 7, 499-533

Abstract: Abstract The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies.

Keywords: Fokker–Planck equation; Pontryagin maximum principle; Non-smooth optimal control problems; Stochastic processes; 35Q84; 49J20; 93E20; 49M05 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-020-00187-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:76:y:2020:i:2:d:10.1007_s10589-020-00187-x

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-020-00187-x

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().